Washing Machine Pump Fault

It sounds like a fault on the neutral return on the water pump. The pump is clearly OK as you've run it separately, and if you know it's getting power, then it must be the neutral return that's not getting through.

It could be a fault at the program control unit (timer), but these are expensive parts. Buying a new timer carries a risk, because no one will sell you one with a guarantee. Therefore, if you replace it and it still doesn't work, or you introduce a fault because you wire it up wrong you have problems.

There is a company that repairs washing machine timers and pcbs, which is another possible option called QER

Alternatively, if your washing machine is less than 5 years old, you could get Hoover to fix it under the free 5 year parts guarantee ( I have a 5 year parts guarantee - should I use it? ) They will supply the part free and charge just the labour which should still be little more than the cost of a new control board.